Investigations On The Construction And Decoding Of Polar Codes

Polar codes are the first class of error correction codes that can asymptotically achieve the capacity of binary-input memoryless output-symmetric channels.Polar codes are the key technology in the next generation mobile communication systems,and they are selected as the channel coding scheme for the control channel in the 5G.In addition to the capacity-achieving property,polar codes have no error floors under successive cancellation(SC)decoding,and the quasi-maximum likelihood decoding performance of polar codes can be achieved by using SC list(SCL)decoder.However,the polar coding technique still needs to be improved,and the main problems of the state-of-the-art polar coding technique are summarized as follows.The SCL decoder is one of the most popular decoders for polar codes.Nevertheless,there exist the following two main drawbacks of the SCL decoder.On the one hand,the SCL decoding is sequential decoding,which may cause the long decoding latency.On the other hand,the SCL decoding is list decoding,which may introduce high complexity if the list size is large.Therefore,the SCL decoder needs to be improved by reducing its decoding latency and complexity.Although the belief propagation(BP)decoding of polar codes can be implemented in parallel,the error rate performance of the BP decoder is inferior to that of the SCL decoder.Hence,the error correction ability of the BP decoder for polar codes should be improved.The concatenated polar codes,such as polar codes concatenated with the cyclic redundancy check(CRC),can achieve better code word distance spectrum compared with single polar codes.However,the structure of the concatenated polar codes is different from the single polar codes.Thus,a specific decoder should be designed for a given concatenated polar code.In addition,combining polar codes with high order modulation is able to increase the information transmission rate.As a result,it is important to investigate how to improve the error rate performance of the polar coded modulation systems.Therefore,in this thesis we investigate the efficient construction and decoding methods for polar codes.The main contributions of this thesis are summarized as follows.Three algorithms are proposed to improve the SCL decoding for polar codes.Firstly,we propose a path-split-reduced SCL decoding scheme for polar codes based on the partial orders between the polarized channels.This path-split-reduced algorithm selects unreliable information bits according to the partial orders between polarized channels.In the SCL decoder,the decoding path only splits at unreliable information bits,while at other information bits,there is no path splitting.Simulation results demonstrate that the proposed path-split-reduced SCL decoding scheme can reduce around 75%path splitting in the SCL process.Secondly,SCL bit flip(SCLF)decoding is proposed to improve the block error rate(BLER)performance of the CRC aided SCL(CA-SCL)decoder without increasing the list size.By the revised critical set and the identification of the path-split status,the proposed SCLF algorithm can perform bit flip in the SCL decoding process.Simulation results exhibit that the proposed SCLF decoder has around 0.2 dB signal-to-noise ratio(SNR)gains compared to the conventional CA-SCL decoder with the same list size.Thirdly,we propose a latency-reduced SCL decoder to further decrease the decoding latency of the SCL decoder.The first consecutive rate 0 and the most significant rate 1 nodes are defined.In addition,the fast decoding algorithms for such nodes are proposed without sacrificing the BLER performance.Further,a suboptimal path metric sorting scheme is introduced to reduce the complexity of the path metric sorting process in the SCL decoder.Simulation results show that the BLER degradation caused by the suboptimal sorting is negligible under the SCL decoder when the CRC is not employed.To improve the BLER of the BP decoding of polar codes,we propose a BP bit-flip(BPF)decoder based on the critical set with order ?(CS-?).If the decoding result of the conventional BP decoder does not satisfy the CRC when the maximum iteration number is reached,the bit-flip decoding is activated.The bit-flip means that the BPF decoder sets the priori knowledge of the bits in the CS-?)to infinity.Simulation results demonstrate that the BPF decoder has 1 dB SNR gains over the conventional BP decoder.In addition,at medium and high SNR points,the latency of the BPF decoder is similar to that of the conventional BP decoder,and much lower than that of the CA-SCL decoder with medium list sizes.To realize the maximum likelihood(ML)decoding of the CRC-polar concatenated codes,we propose a sphere decoder(SD)for CRC-polar codes.By concatenating polar codes with the nonsystematic CRC,the generator matrix of the entire codes has a stair structure,which can be utilized to realize the ML decoding of the CRC-polar codes.In addition,a novel SD radius selection algorithm is proposed to reduce the average complexity of the SD.This radius selection method increases the SD radius monotonously.If the current radius R is small so that the ML code word is not included,the proposed radius selection method will produce a new radius larger than R given the condition that R is a lower bound of the distance between the ML code word and the received signal.Simulation results show that the BLER of the proposed SD is superior to that of the CA-SCL decoder.Compared with the existing radius selection methods,the proposed scheme can reduce more amount of the decoding complexity.The low-complexity construction of polar codes under the multi-level coded(MLC)modulation and bit-interleaved coded modulation(BICM)is proposed.For the MLC,we first analyze the similarity between the MLC modulation and the polarization process of polar codes,and further propose a polar code construction method based on the Bhattacharyya parameter.Due to the multi-stage decoding(MSD)required by the MLC,the decoding under the MLC is inherently of high latency.To reduce such latency,we propose an adaptive CA-SCL decoding method.This adaptive CA-SCL decoding method decodes each component polar code using monotonously increasing list size until the decoding results satisfy the CRC.Simulation results demonstrate that under the MLC,the BLER of the proposed construction algorithm can approach that of the Monte-Carlo scheme.In addition,at medium and high SNR points,the proposed adaptive decoding method can efficiently reduce the decoding latency in the MSD.For the BICM,a novel channel mapping is introduced based on minimizing the summation of the Bhattacharyya parameters of the second half polarized channels in a shorter polar code.Although this channel mapping is suboptimal,simulation results exhibit that the BLER of the proposed channel mapping can approach that of the Monte-Carlo method under the BICM.